Generalized Logistic Models and its orthant tail dependence

The Multivariate Extreme Value distributions have shown their usefulness in environmental studies, financial and insurance mathematics. The Logistic or Gumbel-Hougaard distribution is one of the oldest multivariate extreme value models and it has been extended to asymmetric models. In this paper we introduce generalized logistic multivariate distributions. Our tools are mixtures of copulas and stable mixing variables, extending approaches in Tawn (1990), Joe and Hu (1996) and Foug\`eres et al. (2009). The parametric family of multivariate extreme value distributions considered presents a flexible dependence structure and we compute for it the multivariate tail dependence coefficients considered in Li (2009)

On the variance of the trimmed mean

This note provides a new expression for the variance of the trimmed mean in terms of product moments of order statistics. An exact expression for the bias of the estimator of the variance of trimmed mean is also provided. As an illustration, exact calculations are carried out for small samples from various t-distributions using (Tiku and Kumra, 1985) product moment tables for the order statistics of the t-distribution.Order statistics t-distribution Winsorized mean

Bivariate Distributions with Given Extreme Value Attractor

A new class of bivariate distributions is introduced and studied, which encompasses Archimedean copulas and extreme value distributions as special cases. Its dependence structure is described, its maximum and minimum attractors are determined, and an algorithm is given for generating observations from any member of this class. It is also shown how it is possible to construct distributions in this family with a predetermined extreme value attractor. This construction is used to study via simulation the small-sample behavior of a bivariate threshold method suggested by H. Joe, R. L. Smith, and I. Weissman (1992, J. Roy. Statist. Soc. Ser. B54, 171-183) for estimating the joint distribution of extremes of two random variates.Archimedean copulas, bivariate threshold method, dependence functions, domains of attraction, extreme value distributions